Related papers: Note on Green Function Formalism and Topological I…
We propose a topological order parameter for interacting topological insulators, expressed in terms of the full Green's functions of the interacting system. We show that it is exactly quantized for a time reversal invariant topological…
Green's function zeros, which can emerge only if correlation is strong, have been for long overlooked and believed to be devoid of any physical meaning, unlike Green's function poles. Here, we prove that Green's function zeros instead…
We propose general topological order parameters for interacting insulators in terms of the Green's function at zero frequency. They provide an unified description of various interacting topological insulators including the quantum anomalous…
The one dimensional closed interacting Kitaev chain and the dimerized version are studied. The topological invariants in terms of Green's function are calculated by the density matrix renormalization group method and the exact…
The Chern topological numbers of a material platform are usually written in terms of the Berry curvature, which depends on the normal modes of the system. Here, we use a gauge invariant Green's function method to determine from first…
We propose an order parameter for a general one-dimensional gapped system with an open boundary condition. The order parameter can be computed from the ground state entanglement entropy of some regions near one of the boundaries. Hence, it…
We explicitly calculate the Green functions describing quantum changes of topology in Friedman-Lemaitre-Robertson-Walker Universes whose spacelike sections are compact but endowed with distinct topologies. The calculations are performed…
Topological phase transitions in free fermion systems can be characterized by closing of single-particle gap and change in topological invariants. However, in the presence of electronic interactions, topological phase transitions are more…
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
Partition functions of some two-dimensional statistical models can be represented by means of Grassmann integrals over loops living on two-dimensional torus. It is shown that those Grassmann integrals are topological invariants, which…
We construct a Green function, which can identify the topological nature of interacting systems. It is equivalent to the single-particle Green function of effective non-interacting particles, the Bloch Hamiltonian of which is given by the…
The organization of the electrons in the ground state is classified by means of topological invariants, defined as global properties of the wavefunction. Here we address the Chern number of a two-dimensional insulator and we show that the…
We show that Green function methods can be straightforwardly applied to nonlinear equations appearing as the leading order of a short time expansion. Higher order corrections can be then computed giving a satisfactory agreement with…
Topological insulators are noninteracting, gapped fermionic systems which have gapless boundary excitations. They are characterized by topological invariants, which can be written in many different ways, including in terms of Green's…
Defects which appear in heterostructure junctions involving topological insulators are sources of gapless modes governing the low energy properties of the systems, as recently elucidated by Teo and Kane [Physical Review B82, 115120 (2010)].…
Topological invariants in terms of the Green's function in momentum and real space determine properties of smooth textures within topological media. In space dimension D=1 the topological invariant N_3 in terms of the Green's function…
We review the D-formalism, a new method for determining the renormalization of Green functions to all orders in perturbation theory. This formalism exploits the fact that the renormalized Green functions may be calculated by displacing by…
Here, we develop a gauge-independent Green function approach to characterize the Chern invariants of generic non-Hermitian systems. It is shown that analogous to the Hermitian case, the Chern number can be expressed as an integral of the…
Understanding correlation effects in topological phases of matter is at the forefront of current research in condensed matter physics. Here we try to clarify some subtleties in studying topological behaviors of interacting Weyl semimetals.…
Recent work on the quantization of Maxwell theory has used a non-covariant class of gauge-averaging functionals which include explicitly the effects of the extrinsic-curvature tensor of the boundary, or covariant gauges which, unlike the…